How to Write Progressive Metal - Parts 8-9: Odd Time Signatures and Polymeters

Hey, guys! Kevin Goetz back again with another free YouTube lesson. This time, we're looking to discuss odd time signatures, both on their own, and played against other time signatures; polymeters.
The usual disclaimer: Yes, there are still plenty of topics I haven't covered yet. They'll be covered in their own lessons at their own times, rather than rushed. Please be patient.

Step # 1 - Odd Time Signatures

Before we can construct all those fancy polymeters we're just itching to play, we have to understand why these particular prog "tropes" are so popular. There is no official way to refer to "crazy wonky time signature awesomeness." If I may attempt to sum up every term I've heard: People have said "odd," "unusual," "asymmetric," "irregular," and "complex." The words "meter" and "time signature" are also apparently interchangeable, as far as most people are concerned. For more generalized study of time signatures, head over to the Wikipedia article on Time Signatures. For our purposes, we're looking at very specific, prog-focused odd meter.
Common odd time signatures used in prog include 3/4, 5/4, 7/8, 9/8, 11/8, so on and so forth. Understanding these numbers is, in actuality, extraordinarily simple. For example:
3/4 - Three-four means "three-fourths," or "three quarters." Three quarter-notes. Therefore, following our understanding of notation, there are 6 eighth-notes. 12 sixteenth-notes. Essentially, 3/4 is like chopping off one quarter note, four sixteenth notes, etc.
5/4 - If 3/4 removes a quarter note, 5/4 adds one. Very intuitive.
7/8 - Seven-eighths. "7 eighth-notes." 14 sixteenth-notes. 3.5 quarter-notes. Think of this like chopping off two of your last four sixteenth notes.
9/8 - 9/8 is to 7/8 as 5/4 is to 3/4. You're replacing subtraction with addition. Instead of chopping off two of the last four sixteenth notes, you're adding two sixteenth notes, or one eighth note, onto the end of your 4/4 measure.
Using this formula, you can understand literally any time signature you decide to mess around with. Fire up your Tuxguitar, and start experimenting with the altered rhythms of your riffs, interspersed among 4/4 or other time signatures. Try to really feel the effect that cutting or elongating your riffs has. A good starting point, if you're really not sure where to begin, could be to take the fourth measure of a repeating 4/4 riff and switch it to 5/4, elongating it by one degree.

Step # 2 - Polymeters

Polymeters, put simply, consist of taking these time signatures we've come to understand, and having one instrument play them while another (or several others) plays in standard 4/4, providing a contrast. The instruments playing in an odd meter seems to resolve at different points during the course of the 4/4 groove underneath it. For instance, a riff in 5/4 played over 4/4 drums, would seem to restart one quarter note (four sixteenth notes) after the drums' restarting point, continuously, until it eventually resolves naturally, or you choose to force a resolution. Forced resolution, as a quick side note, is essentially crunching a polymeter back down into 4/4 at the end. Essentially, halfway through the fourth measure, regardless of where your polymeter currently is, you alter the riff in some way (rests, flourishes, whatever works) and then begin it again when the drums start fresh in the next measure.
For some additional information, and plenty of audio examples, take a look at these video lessons. The first is polymeters, the second is odd time signatures.

This video series is updated consistently three times a week, so check that out if you get tired of waiting for new articles.

Haven't checked the videos, but the article is just great at simplifying this subject.
I remember listening to a Meshuggah song and wanting to understand what the hell these guys are doing. And once you break it down and see the different time signatures, you find those are actually easy to work with. It's very basic math, and since you can actually *hear* this math resolve, it becomes a very intuitive thing to implement.

I couldn't deduce your time signature "formula" from your examples. 4/4 is simply four quarter notes, 5/4 is five quarter notes and so on, but it is complicated to think of 7/8 as 14 sixteenth notes. Sure, these are equivalent in some sense, but counting 7/8 with sixteenth notes is far from intuitive. I would actually argue that it would then be 14/16, not 7/8. Similarly, 3/4 is a different time signature. I would also touch the subject of accents which is of great importance in the subject of time signatures.

Well, the only reason I brought up the idea that 7/8 contains 14 sixteenth notes, is due to the common usage of sixteenth notes in prog. If there are seven eighth notes, that's all well and good, but we have to be aware of note equivalency when thinking about how many notes we're working with. I fail to see why thinking of 7/8 with 14 sixteenth notes is any different from 5/4 with 20 sixteenth notes. It's all just notation and equivalency.

I understand that patterns can be harder to see for some. Basically, the way that always works for me is, just remember that each increment is either doubled, or halved. So going from 5/4 and realizing that there are 20 sixteenth notes, is saying, 5/4, 10/8, 20/16. Just double both the numerator and denominator each time you go to a smaller note increment. The numerator represents how many of each note increment exists in a measure of that time signature, and the denominator represents what the note increment is. Of course this is all still 5/4; it's more just a mental trick for considering how many notes we can use in any given time signature. More useful when planning polymeters than when simply trying to compose in an odd time signature. Does that make sense?